{"id":"W4396535099","doi":"10.5539/jmr.v16n2p1","title":"On the Universal Presence of Mathematics for Incompletely Predictable Problems in Rigorous Proofs for Riemann Hypothesis, Modified Polignac’s and Twin Prime Conjectures","year":2024,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"History and Theory of Mathematics","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Mathematical proof; Riemann hypothesis; Prime (order theory); Prime number theorem; Twin prime; Prime number; Calculus (dental); Pure mathematics; Discrete mathematics; Combinatorics; Geometry","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaresearch"],"consensus_categories":[],"category_scores_codex":[0.01267771,0.0003431608,0.0009804415,0.0008081914,0.0002623444,0.0001567439,0.0009421965,0.0002232351,0.00004118519],"category_scores_gemma":[0.01010688,0.0002217882,0.0002920692,0.0004448138,0.0005729123,0.0002345017,0.0001551162,0.0008050845,0.000004568885],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002310769,"about_ca_system_score_gemma":0.0004744504,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008337104,"about_ca_topic_score_gemma":0.00002350966,"domain_scores_codex":[0.995827,0.0003738393,0.001557655,0.0003078065,0.00129253,0.0006411203],"domain_scores_gemma":[0.9658659,0.03198544,0.0006687813,0.0005844323,0.0007397879,0.0001556443],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000191295,0.001517024,0.000003791402,0.01377611,0.0003311243,0.00002081142,0.0229021,0.0002866099,0.003102928,0.9483334,0.009009962,0.0005247729],"study_design_scores_gemma":[0.00102619,0.001067002,0.000002828573,0.003594282,0.0001206434,0.0001207141,0.003677651,0.03567689,0.004158218,0.9493006,0.001045529,0.0002093836],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7540712,0.003075402,0.2240721,0.002164961,0.0004714346,0.01055892,0.0003118248,0.0001172816,0.005156862],"genre_scores_gemma":[0.8937987,0.0001240787,0.1036998,0.00002208284,0.0001983491,0.0002409493,0.000001852227,0.0001529675,0.001761233],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1397274,"threshold_uncertainty_score":0.9982314,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1790120488527892,"score_gpt":0.3733470735226845,"score_spread":0.1943350246698953,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}